A test for a certain rare disease is assumed to be correct 95% of the time: if a person has the disease, the test result is positive with probability 0.95, and if the person does not have the disease, the test result is negative with probability 0.95. A person drawn at random from a certain population has probability 0.001 of having the disease.

Question

Find the probability that a random person tests positive. (This answer will require an accuracy of 4 decimal places.)


Given that the person just tested positive, what is the probability he actually has the disease?

Answer 1

0.0187